# Questions relating to time dilation

1. Oct 13, 2012

### salzrah

1. Is there anyway we can measure time without depending on or using light? If we can, what are they and do special relativistic effects still take place in "close to c" relative velocity situations by using this method of time keeping?

2. My second question relates to relative movement. Time dilation suggests that the time measured in two different reference frames moving with a relative velocity to each other is different. This conclusion then suggests that the time measured in a moving reference frame relative to a stationary one is less than the time measured by the stationary observer for the moving reference frame. Because both frames are moving relative to each other, doesn't the reference frame which we originally dictate to be the one moving see that time actually slows down in the reference frame that we considered to be stationary? This is because the velocity that we assumed one reference frame had relative to another can be applied to the other reference frame in the opposite direction. Therefore, we can assume both reference frames believe the other reference frame has a slower passage of time. If what I said so far is true, then at any instant the amount of time that has passed for each observer in their own reference frame is the same and each observer believes less time has passed in the other reference frame. (This contradiction relates to the twin paradox, without the acceleration part that many use as a "solution" to the paradox.) Now I want to know, is what I have said a paradox? If it is, what does this suggest? One thing it can suggest is that the way we measure time is flawed. But what else can be said about the nature of time?

2. Oct 13, 2012

### bcrowell

Staff Emeritus
Yes, e.g., a mechanical clock, or the earth's rotation.

Yes.

3. Oct 13, 2012

### Erland

The second question has to do with the relativity of simultaneity.

The first question, I leave to our one-way and two-way measurement experts to sort out. :)

4. Oct 13, 2012

### Staff: Mentor

The bolded words in the quote above are the crux of the problem.

You have to consider not only time dilation but also the relativity of simultaneity, and when you do that the apparent paradoxical inconsistency goes away. There are a number of more thorough explanations in other threads here and on the web - try googling for "relativity of simultaneity", see what you find, and if that doesn't clear things up for you, come back with a more specific question and we can help.

5. Oct 13, 2012

### salzrah

Ben, how can we theoretically prove that time measuring techniques that do not rely on light still have special relativistic effects? An explanation of why you said "yes" would be great.

Erland, the example post you provided suggests that both the train master and the train driver accuse each other of aging slower and "that is no contradiction." But the contradiction is that the train master/driver age slower in one reference frame and faster in another. How is that not a contradiction?

6. Oct 13, 2012

### bcrowell

Staff Emeritus
Theoretically, it follows from the fact that SR is a description of time and space themselves, not of specific measuring sticks or types of clocks. SR doesn't predict different length contractions for wooden rulers than for aluminum rulers, and we can see this because SR doesn't have any descriptions of wood or aluminum, just space. Ditto for a wound-spring clock versus a light clock.

Experimentally, a good example is decay of relativistic muons, Bailey at al., Nucl. Phys. B150(1979) 1. Description here: http://www.lightandmatter.com/html_books/lm/ch23/ch23.html#Section23.1 [Broken] (example 4).

You may have gotten the wrong impression from the common pedagogical use of the "light clock" as a way of introducing SR. The light clock doesn't actually exist, and it plays no fundamental role in relativity. You may also have gotten the impression that light itself plays some fundamental role in relativity. The modern point of view is that it doesn't. The fact that Einstein's 1905 postulates referred to light was just an artifact of people's limited understanding of fundamental particles and fields in 1905.

Last edited by a moderator: May 6, 2017
7. Oct 13, 2012

### Erland

Because they have different opinions of which events are simultaneous and not.
The event when the clock at the west end (where the station master is located) shows 2 and the event when the clock at the east end shows 2 are simultaneous wrt the platform. Since at the second of these events, the clock in the locomotive (which arrives to the east end at this precise moment) shows 1, the station master says that the train driver has been aging slower. Notice that we must talk about two events here, since the station master and the train driver are not located at the same point in space. For the station master to reach his conclusion, it is necessary that the two events are simultaneous, according to him.

But, according to the train driver, these two events are not simultaneous. The train driver must use two other events, which are simultaneous wrt the train, to find out which one is aging slower, and these two events are not simultaneous wrt the platform (and the station master). It is therefore not a contradiction that they reach different conclusions about who is aging slower.

8. Oct 13, 2012

### salzrah

Ben, if we used a wound-spring clock, then how can you theoretically prove time dilation still occurs. Everyone suggests time dilation occurs independently of the way we measure time, but I have not found any theoretical proof of time dilation without using light clocks. Atomic clocks use microwaves, which is why they are compared to light clocks -- both rely on the propagation of EM waves, which I agree should show time dilation at high speeds. The experiment you cite uses atomic clocks as well. I have read on decaying muons for some time and have yet to find one experiment where atomic clocks are not used.

I understand the relativity of simultaneity much better now. Erland, I completely understand why the train driver and master think the other has aged more which is a direct consequence of time dilation. However, in Erland's example you simply say the west end clock in the train shows t=4. Why does it show t=4? Why would it show any time different that the other clock on the train?...
Other explanations of this idea use the lightning bolt example on the front end and back end of a train. Like this -- .
But, if the lady on the train accounts for her speed relative to the lightning bolt and how long it takes to reach her eyes, can't she calculate the proper time of the lightning bolt and find when it actually occurred? The part I don't understand is that just because she SEES the lightning at different times does not imply that in her reference frame the lightning bolts struck at different times. The same way when we see stars that are already dead doesn't mean they are alive to us because we are seeing them right now.

I hope readers understand that I am not arguing against time dilation, but want proof of time dilation that doesn't rely on EM waves. And I am not arguing against the relativity of simultaneity, but asking why there can't be an event that two observers in different moving reference frames experience at their own respective instantaneous present.

Nugatory, why can there not be a NOW when the times on both clocks are measured? If there is an observer that sees two objects moving relative to each other and measures the clocks at an instantaneous moment in the present state then how does the relativity of simultaneity apply?

Last edited by a moderator: Sep 25, 2014
9. Oct 13, 2012

### Erland

This can be calculated by the Lorentz transformation.
According to the passenger, she is at rest, so she has no speed to account for. Also, light speed is c relative to her, no matter in what direction it propagates. (We have now applied both fundamental postulates of SR.) The light from both flashes travel the same distance according to her, half the length of the train (although in opposite directions). Since she sees the front flash before the back flash, she must therefore conclude that the front flash struck before the back flash (and of course, she knows that each flash strikes before she sees it).
I'm afraid that's not possible, since the invariance of light speed (that is, the speed of EM waves) is a fundamental postulate of SR.

Last edited by a moderator: Sep 25, 2014
10. Oct 13, 2012

### Staff: Mentor

The problem is that all the observers have their own equally valid NOW.

Say I'm floating in space, and suddenly two spaceships zoom past me, each traveling at .6c, one moving left to right and the other moving right to left. As they pass in front of me, all three of us set our clocks to zero.

Then I wait for 100 seconds by my clock. At the exact moment that my clock reads 100 seconds, both of the spaceship clocks will read 80 seconds, for me, using my frame's notion of simultaneity. (How I actually know what their clocks say is a non-trivial problem - we can go there later). So I'll say that at the exact moment that the left-mover's clock reads 80, my clock reads 100. I also say that his clock is running slower than mine, because his ticked off 80 seconds since they were synchronized while mine ticked off 100.

But what about the guy on the left moving spaceship? For him, at the exact moment that his clock reads 80, my clock reads 64 and he says that my clock is running slow. That's relativity of simultaneity at work: to him, 80 on his clock and 64 on mine are simultaneous, while for me 80 on his clock and 100 on mine are simultaneous.

Meanwhile, we've still got this other spaceship zooming off to the right. I'll say that when my clock reads 100, his clock reads 80, just like left-mover's clock. But when right-mover sees his clock reading 80, he won't say that mine reads 100 and left-mover's reads 80. He'll say that my clock reads 64 at the moment that his reads 80, and that left-mover's reads something less than 64.

So we all end up seeing everyone else's clock running slow relative to ours, yet there is no paradox.

11. Oct 13, 2012

### salzrah

So the amount of time progressed at the back end of the train is different from the time progressed at the front of the train? How does that even intuitively make sense?

The only reason she sees the front flash first is because of her velocity relative to the flash. She is traveling towards the front flash so she sees it before. If she accounts for her speed relative to the flashes she will determine the flashes occurred at the same time but she saw one first. This does not mean it occurred first.

Oh my...I know light speed is invariant. I know it is a fundamental postulate of SR. I am talking about proving time dilation without using EM waves to measure that time.

12. Oct 13, 2012

### salzrah

Nugatory, how can "all the observers have their own equally valid NOW."?
Isn't the present an all encompassing instantaneous event for everything in the universe. One object can not, not be in the present while another is in the present. I like your example, and yes I understand that we observe the time in another reference frame to move slower if that frame is moving with a velocity relative to you. However, the contradiction is still there. In one reference frame the time progressed in one reference frame is less than what an observer in another reference frame measures it to be. The reason I brought up this "contradiction" is that when people say time moves slowly at close to c speeds, it does not mean that things in the "moving" reference frame will actually move slower to the "stationary" reference frame. Just the time the "stationary" frame measures to pass will be different then the time measured in the "moving" frame. The actual time passed will be equal if both reference frames measure their own time passage.

13. Oct 13, 2012

### Staff: Mentor

Just as you say, she must allow for the time for light to travel between the point of the strike and her eyes, and adjust her notion of when the strike happened accordingly.

But if light always travels at the speed c, and if both strikes happened at the same distance D from her... Then that travel time will be D/c for both strikes, so she makes the same adjustment for both strikes. With the same adjustment, there's no way that the light can reach her eyes at different times if the strikes were simultaneous.

14. Oct 13, 2012

### salzrah

Yes, but while the two light flashes are traveling towards her, she is not still. She is moving away from one light flash and towards another. So she sees the front one first, even though they occurred at the same time.
To better put it -- the back light flash must travel a greater distance than the front flash.

15. Oct 13, 2012

### Staff: Mentor

No. It's weird, it's counter-intuitive, it goes against everything we've learned in a lifetime experiencing speeds that are small compared with the speed of light.... But nonetheless, there are no all-encompassing instantaneous events for everything in the universe.

That's what "relativity of simultaneity" means. You can't say that two things happen "now" without also implying that they're happening at the same time (that time being now, of course). If "at the same time" is relative, then there's no universal now.

16. Oct 13, 2012

### Erland

No, it is not so! An event is given by three space and one time coordinate (x,y,z,t), although the coordinates depend of the reference system. If we change the space coordinates of an event, we get another event, even if the time coordinate remains unchanged. If I am sleeping in my bed the very moment you read this, these (my sleeping and your redaing) are different events even if they are simultaneous (wrt us observers on Earth). An observer in a reference system moving with a high speed wrt us will not consider these two events as simultaneous.

There is no such thing as "an all encompassing instantaneous event for everything in the universe". The present, wrt us, is an infinite set of events which are simultaneous wrt us but not wrt observers in motion wrt us. Such an observer has another "present".

17. Oct 13, 2012

### Staff: Mentor

But suppose I choose a point of view in which she's not moving? She and the train are at rest, while the ground is moving backwards. So a lightning flash hits both ends of this stationary train, and the lady in the middle of the train will see the flashes if and only if they happened at the same time. But the the observer on the platform, which is moving backwards while the train is at rest, will not see the flashes at the same time.

What makes the platform observer's assertion that the flashes were not simultaneous any more right than the train lady's assertion that they were?

18. Oct 13, 2012

### Erland

But she is still! In the reference system at rest wrt the train, that is. And this reference system is precisely as valid as the one at rest wrt the platform. This is what the special principle of relativity says.

19. Oct 13, 2012

### salzrah

"You can't say that two things happen "now" without also implying that they're happening at the same time"

Time is relative because of the way we measure time. The present is independent of time. If one event occurs NOW, it occurs NOW for every frame of reference. We just MEASURE the time that the event occurs differently. An event can not happen in the present for a reference frame while it has already happened or will happen in another frame.
I may be wrong in saying what I have stated, but every example I see disregards that the object that is moving has to account for its movement relative to the light flashes to see when the light flashes ACTUALLY occurred. If you can provide me a better example proving the relativity of simultaneity it would be great!

20. Oct 13, 2012

### salzrah

She is not still relative to the light flashes. I don't know if you watched the youtube video I posted, but the flashes of light hit the ground from the sky. The train/lady has a velocity with respect to the flashes.